HRZZ Research Project

Codes and Related Combinatorial Structures

(2014-2018)

University of Rijeka - Department of Mathematics

 
 

About the project
 

 

Papers:

  • D. Crnković, D. Dumičić Danilović, S. Rukavina, M. Šimac, On some new Steiner 2-designs S(2,5,45), Util. Math. 111 (2019), 281-308.

  • R. Egan, P. Ó Catháin, Morphisms of Butson classes, Linear Algebra Appl. 577 (2019), 78-93.

  • R. Egan, P. Ó Catháin, E. Swartz, Spectra of Hadamard matrices, Australas. J. Combin. 73 (2019), 501-512.

  • D. Crnković, A. Švob, Transitive t-designs and strongly regular graphs constructed from linear groups L(2,q), q <= 23, Int. J. Group Theory 8 (2019), 43-64.

  • R. Egan, Phased unitary Golay pairs, Butson Hadamard matrices and a conjecture of Ito's, Des. Codes Cryptogr. 87 (2019), 67-74.

  • D. Crnković, V. Mikulić Crnković, A. Švob, Block designs and strongly regular graphs admitting a transitive action of the Mathieu group $M_11$, Australas. J. Combin. 73 (2019), 149-161.

  • D. Crnković, R. Egan, A. Švob, Constructing self-orthogonal and Hermitian self-orthogonal codes via weighing matrices and orbit matrices, Finite Fields Appl. 55 (2019), 64-77.

  • D. Crnković, D. Dumičić Danilović, S. Rukavina, On symmetric (78,22,6) designs and related self-orthogonal codes, Util. Math. 109 (2018), 227-253.

  • D. Crnković, R. Egan, A note on Siamese twin designs intersecting in a BIBD and a PBD, Math. Comput. Sci. 12 (2018), 389-395.

  • D. Dumičić Danilović, On some new resolvable 1-rotational (45,5,2)-BIBDs, Bull. Inst. Combin. Appl. 84 (2018), 53-64.

  • D. Crnković, N. Mostarac, Self-dual codes from orbit matrices and quotient matrices of combinatorial designs, Discrete Math. 341 (2018), 3331-3343.

  • D. Crnković, V. Mikulić Crnković, A. Švob, Transitive combinatorial structures invariant under some subgroups of S(6,2) and related codes, Atti Accad. Peloritana Pericolanti Cl. Sci. Fis. Mat. Natur. 96, No. S2, A6 (2018), 15 pages.

  • D. Crnković, M. Maksimović, S. Rukavina, Codes from orbit matrices of strongly regular graphs, Rad Hrvat. Akad. Znan. Umjet. Mat. Znan. 22(536) (2018), 23-38.

  • K. Tabak, Normalized difference set tiling conjecture, J. Combin. Des. 26 (2018), 505-513.

  • D. Crnković, V. Mikulić Crnković, B. G. Rodrigues, On self-orthogonal designs and codes related to Held's simple group, Adv. Math. Commun. 12 (2018), 607-628.

  • D. Crnković, S. Rukavina, A. Švob, New strongly regular graphs from orthogonal groups $O^+(6,2)$ and $O^-(6,2)$, Discrete Math. 341 (2018), 2723-2728.

  • M. Maksimović, Enumeration of Strongly Regular Graphs on up to 50 Vertices Having S_3 as an Automorphism Group, Symmetry 10(6), 212 (2018).

  • V. Krčadinac, Some new designs with prescribed automorphism groups, J. Combin. Des. 26 (2018), 193-200.

  • V. Krčadinac, M. O. Pavčević, New small 4-designs with nonabelian automorphism groups, in: Mathematical Aspects of Computer and Information Sciences, (J. Blömer, I. S. Kotsireas, T. Kutsia, D. S. Simos, Eds.), Lecture Notes in Computer Science, Springer, Cham, 2017, 289-295.

  • D. Crnković, R. Egan, A. Švob, Orbit matrices of Hadamard matrices and related codes, Discrete Math. 341 (2018), 1199-1209.

  • O. W. Gnilke, M. Greferath M. O. Pavčević, Mosaics of combinatorial designs, Des. Codes Cryptogr. 86 (2018), 85-95.

  • D. Crnković, N. Mostarac, PD-sets for codes related to flag-transitive symmetric designs, Trans. Comb. 7 (2018), 37-50.

  • D. Crnković, Regular Hadamard matrices constructed from Hadamard 2-designs and conference graphs, Discrete Math. 341 (2018), 520-524.

  • R. Egan, On equivalence of negaperiodic Golay pairs, Des. Codes Cryptogr. 85 (2017), 523-532.

  • D. Crnković, V. Mikulić Crnković, A. Švob, New 3-designs and 2-designs having U(3,3) as an automorphism group, Discrete Math. 340 (2017), 2507-2515.

  • D. Crnković, B. G. Rodrigues, S. Rukavina, V. D. Tonchev, Quasi-symmetric 2-(64,24,46) designs derived from AG(3,4), Discrete Math. 340 (2017), 2472-2478.

  • A. Nakić, L. Storme, Tight sets in finite classical polar spaces, Adv. Geom. 17 (2017), 109-129.

  • D. Crnković, S. Rukavina, L. Simčić, On triplanes of order twelve admitting an automorphism of order six and their binary and ternary codes, Util. Math. 103 (2017), 23-40.

  • K. Tabak, M. O. Pavčević, CZ-groups, Glas. Mat. Ser. III 51 (2016), 345-358.

  • V. Krčadinac, R. Vlahović, New quasi-symmetric designs by the Kramer-Mesner method, Discrete Math. 339 (2016), 2884-2890.

  • D. Crnković, D. Dumičić Danilović, S. Rukavina, Enumeration of symmetric (45,12,3) designs with nontrivial automorphisms, J. Algebra Comb. Discrete Struct. Appl. 3 (2016), 145-154.

  • D. Crnković, M. Maksimović, B. G. Rodrigues, S. Rukavina, Self-orthogonal codes from the strongly regular graphs on up to 40 vertices, Adv. Math. Commun. 10 (2016), 555-582.

  • D. Crnković, V. Mikulić Crnković, A. Švob, On some transitive combinatorial structures and codes constructed from the symplectic group S(6,2), J. Combin. Math. Combin. Comput. 97 (2016), 119-138.

  • F. Cvitić, M. O. Pavčević, J. Pibernik, Bar code standardization by creating new symbology, Tehnički vjesnik - Technical Gazette 23/2 (2016), 511-518

  • D. Crnković, S. Rukavina, Self-dual codes from extended orbit matrices of symmetric designs, Des. Codes Cryptogr. 79 (2016), 113-120.

  • D. Crnković, N. Mostarac, S. Rukavina, Self-dual codes from quotient matrices of symmetric divisible designs with the dual property, Discrete Math. 339 (2016), 409-414.

  • M. De Boeck, L. Storme, A. Švob, The Cameron-Liebler problem for sets, Discrete Math. 339 (2016), 470-474.

  • D. Crnković, H. Kharaghani, Divisible design digraphs, in: Algebraic Design Theory and Hadamard Matrices, (C. J. Colbourn, Ed.), Springer Proc. Math. Stat., Vol. 133, Springer, New York, 2015, 43-60.

  • D. Crnković, S. Rukavina, V. D. Tonchev, New symmetric (61,16,4) designs obtained from codes, in: Algebraic Design Theory and Hadamard Matrices, (C. J. Colbourn, Ed.), Springer Proc. Math. Stat., Vol. 133, Springer, New York, 2015, 61-69.

  • A. Ćustić, V. Krčadinac, Y. Zhou, Tiling groups with difference sets, Electron. J. Combin. 22 (2015)

  • D. Crnković, W. H. Haemers, Walk-regular divisible design graphs, Des. Codes Cryptogr. 72 (2014), 165-175.

  • D. Crnković, Classes of self-orthogonal or self-dual codes from orbit matrices of Menon designs, Discrete Math. 327 (2014), 91-95.

  • D. Crnković, V. Mikulić Crnković, A. Švob, On some transitive combinatorial structures constructed from the unitary group U(3,3), J. Statist. Plann. Inference 144 (2014), 19-40

 

Talks:

  • D. Crnković, On some regular Hadamard matrices and associated codes, Combinatorics 2018, Arco, Italy, June 3-9, 2018.

  • S. Rukavina, Codes from orbit matrices of strongly regular graphs, Combinatorics 2018, Arco, Italy, June 3-9, 2018.

  • N. Mostarac, Self-dual codes from orbit matrices and quotient matrices of combinatorial designs, Graphs, groups, and more: celebrating Brian Alspach's 80th and Dragan Marušič's 65th birthdays,Koper, Slovenia, May 28 - June 1, 2018.

  • M. Maksimović, Self-orthogonal codes from orbit matrices of strongly regular graphs, Graphs, groups, and more: celebrating Brian Alspach's 80th and Dragan Marušič's 65th birthdays,Koper, Slovenia, May 28 - June 1, 2018.

  • V. Mikulić Crnković, On combinatorial structures constructed from unitary groups U(3,q), q= 3,4,5,7, 5th International Combinatorics Conference (5ICC), Melbourne, Australia, December 4-9, 2017.

  • V. Krčadinac, An updated table of quasi-symmetric designs, Colloquium on Combinatorics, Paderborn, Germany, November 24-25, 2017.

  • M. Šimac, LDPC codes constructed from Moore graphs with diameter 2, Colloquium on Combinatorics, Paderborn, Germany, November 24-25, 2017.

  • M. O. Pavčević, New Small 4-designs with Nonabelian Automorphism Groups, 7th International Conference on Mathematical Aspects of Computer and Information Sciences (MACIS 2017), Vienna, Austria, November 15-17, 2017.

  • D. Crnković, A construction of regular Hadamard matrices and related codes, 5th Workshop on Real and Complex Hadamard Matrices and Applications, Budapest, Hungary, July 10-14, 2017.

  • R. Egan, Phased unitaries and a conjecture of Ito’s, 5th Workshop on Real and Complex Hadamard Matrices and Applications, Budapest, Hungary, July 10-14, 2017.

  • D. Crnković, A construction of regular Hadamard matrices, The Second Malta Conference in Graph Theory and Combinatorics, Qawra, Malta, June 26-30, 2017

  • S. Rukavina, Quasi-symmetric 2-(64,24,46) designs derived from AG(3,4), The Second Malta Conference in Graph Theory and Combinatorics, Qawra, Malta, June 26-30, 2017

  • S. Rukavina, The construction of combinatorial structures and linear codes from orbit matrices of strongly regular graphs, Hypergraphs, Graphs and Designs, Sant'Alessio Siculo, Italy, June 21-24, 2017

  • A. Nakić, On the extendability of particular classes of constant dimension codes, Hypergraphs, Graphs and Designs, Sant'Alessio Siculo, Italy, June 21-24, 2017

  • K. Tabak, Normalized tiling conjecture, general abelian case, Colloquium on Combinatorics, Paderborn, Germany, November 4-5, 2016

  • D. Dumičić Danilović, Application of a genetic algorithm on block designs, Colloquium on Combinatorics, Paderborn, Germany, November 4-5, 2016

  • M. Maksimović, Construction of codes from orbit matrices of strongly regular graphs, Colloquium on Combinatorics, Paderborn, Germany, November 4-5, 2016

  • M. Šimac, Absorbing sets in the Tanner graphs of LDPC codes derived from μ-geodetic graphs, 2016 PhD Summer School in Discrete Mathematics, Rogla, Slovenia, June 26 - July 2, 2016

  • D. Dumičić Danilović, On construction of 2-designs and related self-orthogonal codes, 6th Croatian Mathematical Congress, Zagreb, Croatia, June 14-17, 2016

  • M. Maksimović, Form orbit matrices to strongly regular graphs and codes, 6th Croatian Mathematical Congress, Zagreb, Croatia, June 14-17, 2016

  • V. Mikulić Crnković, On some codes invariant under the action of the Held group, 6th Croatian Mathematical Congress, Zagreb, Croatia, June 14-17, 2016

  • D. Crnković, Regular Hadamard matrices, 12th Nordic Combinatorial Conference (NORCOM), Levi, Kittilä, Finland, June 13-15, 2016

  • K. Tabak, Normalized tiling in Zp and NTC conjecture, 12th Nordic Combinatorial Conference (NORCOM), Levi, Kittilä, Finland, June 13-15, 2016

  • R. Vlahović, The Kramer-Mesner Method for Quasi-symmetric Designs, 3rd Istanbul Design Theory, Graph Theory and Combinatorics Workshop, Koç University, Istanbul, Turkey, June 12-17, 2016

  • M. O. Pavčević, Mosaics of Designs, Combinatorics 2016, Maratea, Italy, May 29 - June 4, 2016

  • V. Mikulić Crnković, On self-orthogonal codes generated by orbit matrices of 1-designs, Network Coding and Designs, Dubrovnik, Croatia, April 4-8, 2016

  • M. Šimac, LDPC codes based on μ-geodetic graphs, Network Coding and Designs, Dubrovnik, Croatia, April 4-8, 2016

  • S. Rukavina, Orbit matrices of symmetric designs and related self-dual codes, Symmetries and Covers of Discrete Objects, Queenstown, New Zealand, 14-19 February 2016.

  • V. Mikulić Crnković, On self-orthogonal binary codes invariant under the action of the Held group, Design and Application of Random Network Codes, Istanbul, Turkey, November 4-6, 2015.

  • D. Crnković, Transitive designs constructed from finite groups and related codes, CIMPA Research School Algebraic Representation Theory 2015, Cape Town, South Africa, July 19-31, 2015.

  • D. Dumičić Danilović, Construction of block designs admitting a solvable automorphism group, PhD Summer School in Discrete Mathematics, Rogla, Slovenia, June 27 - July 3, 2015

  • M. Maksimović, Orbit matrices of strongly regular graphs, PhD Summer School in Discrete Mathematics, Rogla, Slovenia, June 27 - July 3, 2015

  • N. Mostarac, Self-dual codes from quotient matrices of symmetric divisible designs with the dual property, PhD Summer School in Discrete Mathematics, Rogla, Slovenia, June 27 - July 3, 2015

  • M. Šimac, LDPC codes based on $\mu$-geodetic graphs obtained from block designs, PhD Summer School in Discrete Mathematics, Rogla, Slovenia, June 27 - July 3, 2015

  • V. Mikulić Crnković, On the construction of non-transitive graphs from groups, 8th Slovenian Conference on Graph Theory, Kranjska Gora, Slovenia, June 21 - 27, 2015

  • A. Nakić, Searching for designs over finite fields with non-trivial automorphism groups, 8th Slovenian Conference on Graph Theory, Kranjska Gora, Slovenia, June 21 - 27, 2015

  • S. Rukavina, Some properties of k-geodetic graphs, 8th Slovenian Conference on Graph Theory, Kranjska Gora, Slovenia, June 21 - 27, 2015

  • D. Crnković, On some Menon designs and related structures, ALCOMA15, Kloster Banz, Germany, March 15-20, 2015

  • D. Dumičić Danilović, Construction of block designs admitting a solvable automorphism group, ALCOMA15, Kloster Banz, Germany, March 15-20, 2015

  • S. Rukavina, Self-dual codes from extended orbit matrices of symmetric designs, ALCOMA15, Kloster Banz, Germany, March 15-20, 2015

  • K. Tabak, Norm invariance method and application, ALCOMA15, Kloster Banz, Germany, March 15-20, 2015

  • D. Crnković, Self-orthogonal or self-dual codes from orbit matrices of block designs, Mathematics of Communications: Sequences, Codes and Designs, Banff, Canada, January 25-30, 2015

 

Poster presentation:

  • A. Švob, Construction of designs from the unitary group U(3,3), Workshop on permutation groups: methods and applications, Bielefeld, Germany, January 12-14, 2017

  • V. Mikulić Crnković, Self-orthogonal designs and codes from Held's group, Workshop on permutation groups: methods and applications, Bielefeld, Germany, January 12-14, 2017

 

PhD theses:

  • N. Mostarac, Self-dual codes and PD-sets constructed from combinatorial designs, October 25, 2017

  • M. Šimac, LDPC codes constructed from some combinatorial structures, March 23, 2017

  • M. Maksimović, Orbit matrices of strongly regular graphs, March 23, 2015

  • D. Dumičić Danilović, The generalisation and the refinement of some algorithms for the construction of block designs and the research for their substructures, November 20, 2014